Average Error: 0.4 → 0.3
Time: 2.6m
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1}{\pi}}{t} - \frac{\frac{\left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{\left(1 - \left(v \cdot v\right) \cdot 3\right) \cdot 2}}}{1 - v \cdot v}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{\frac{\frac{\frac{1}{\pi}}{t} - \frac{\frac{\left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{\left(1 - \left(v \cdot v\right) \cdot 3\right) \cdot 2}}}{1 - v \cdot v}
double f(double v, double t) {
        double r48137525 = 1.0;
        double r48137526 = 5.0;
        double r48137527 = v;
        double r48137528 = r48137527 * r48137527;
        double r48137529 = r48137526 * r48137528;
        double r48137530 = r48137525 - r48137529;
        double r48137531 = atan2(1.0, 0.0);
        double r48137532 = t;
        double r48137533 = r48137531 * r48137532;
        double r48137534 = 2.0;
        double r48137535 = 3.0;
        double r48137536 = r48137535 * r48137528;
        double r48137537 = r48137525 - r48137536;
        double r48137538 = r48137534 * r48137537;
        double r48137539 = sqrt(r48137538);
        double r48137540 = r48137533 * r48137539;
        double r48137541 = r48137525 - r48137528;
        double r48137542 = r48137540 * r48137541;
        double r48137543 = r48137530 / r48137542;
        return r48137543;
}
↓
double f(double v, double t) {
        double r48137544 = 1.0;
        double r48137545 = atan2(1.0, 0.0);
        double r48137546 = r48137544 / r48137545;
        double r48137547 = t;
        double r48137548 = r48137546 / r48137547;
        double r48137549 = v;
        double r48137550 = r48137549 * r48137549;
        double r48137551 = 5.0;
        double r48137552 = r48137550 * r48137551;
        double r48137553 = r48137552 / r48137545;
        double r48137554 = r48137553 / r48137547;
        double r48137555 = r48137548 - r48137554;
        double r48137556 = 3.0;
        double r48137557 = r48137550 * r48137556;
        double r48137558 = r48137544 - r48137557;
        double r48137559 = 2.0;
        double r48137560 = r48137558 * r48137559;
        double r48137561 = sqrt(r48137560);
        double r48137562 = r48137555 / r48137561;
        double r48137563 = r48137544 - r48137550;
        double r48137564 = r48137562 / r48137563;
        return r48137564;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
  2. Using strategy rm

  3. Applied associate-/r*0.4

    \[\leadsto \color{blue}{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.4

    \[\leadsto \frac{\color{blue}{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\pi \cdot t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}}{1 - v \cdot v}\]
  6. Using strategy rm

  7. Applied associate-/r*0.3

    \[\leadsto \frac{\frac{\color{blue}{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\pi}}{t}}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]
  8. Using strategy rm

  9. Applied div-sub0.3

    \[\leadsto \frac{\frac{\frac{\color{blue}{\frac{1}{\pi} - \frac{5 \cdot \left(v \cdot v\right)}{\pi}}}{t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]

  10. Applied div-sub0.3

    \[\leadsto \frac{\frac{\color{blue}{\frac{\frac{1}{\pi}}{t} - \frac{\frac{5 \cdot \left(v \cdot v\right)}{\pi}}{t}}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]

  11. Final simplification0.3

    \[\leadsto \frac{\frac{\frac{\frac{1}{\pi}}{t} - \frac{\frac{\left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{\left(1 - \left(v \cdot v\right) \cdot 3\right) \cdot 2}}}{1 - v \cdot v}\]

Reproduce

herbie shell --seed 2019107 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))